相関係数

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import numpy as np

np.random.seed(777)
x = np.linspace(0, 100, 40) + np.random.rand(40)
y = np.linspace(1, 50, 40) + np.random.rand(40)

coef = np.corrcoef(x, y)
print(np.round(coef, 3))

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import matplotlib.pyplot as plt

plt.figure(figsize=(5, 5))
plt.scatter(x, y)
plt.xlabel("x")
plt.ylabel("y")
plt.title("Scatter plot and correlation coefficient")
plt.grid(alpha=0.3)
plt.show()

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import seaborn as sns

iris = sns.load_dataset("iris")
correlation = iris.corr(numeric_only=True)
correlation

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import matplotlib.pyplot as plt

correlation["sepal_length"].plot.bar(
    grid=True, ylabel="corr", color="#2563eb", title="Correlation with sepal_length"
)
plt.tight_layout()
plt.show()

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import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets

circle, _ = datasets.make_circles(n_samples=1_000, factor=0.1, noise=0.05, random_state=0)
moon, _ = datasets.make_moons(n_samples=1_000, noise=0.05, random_state=0)

def scatter_with_corr(ax, data, title):
    corr = np.corrcoef(data[:, 0], data[:, 1])[0, 1]
    ax.scatter(data[:, 0], data[:, 1], s=10, alpha=0.6)
    ax.set_title(f"{title}\ncorrelation={corr:.2f}")
    ax.set_xticks([])
    ax.set_yticks([])

fig, axes = plt.subplots(1, 2, figsize=(10, 4))
scatter_with_corr(axes[0], circle, "Concentric circles")
scatter_with_corr(axes[1], moon, "Moon-shaped data")
plt.tight_layout()
plt.show()

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import numpy as np
import matplotlib.pyplot as plt

np.random.seed(123)
days = np.arange(365)
season = np.sin(2 * np.pi * days / 365)  # 季節を表す共通要因

ice_sales = 50 + 30 * season + np.random.normal(scale=5, size=days.size)
sunscreen_sales = 40 + 35 * season + np.random.normal(scale=6, size=days.size)

correlation = np.corrcoef(ice_sales, sunscreen_sales)[0, 1]
print(f"Correlation = {correlation:.3f}")

plt.figure(figsize=(6, 5))
plt.scatter(ice_sales, sunscreen_sales, alpha=0.6, s=18, color="#f97316")
plt.xlabel("Ice cream sales")
plt.ylabel("Sunscreen sales")
plt.title("Spurious correlation driven by the same seasonality")
plt.grid(alpha=0.3)
plt.tight_layout()
plt.show()